Physics-Informed and Data-Driven Modelling in Engineering: A Theoretical Framework for Choosing Between Mechanistic, Machine-Learning and Hybrid Approaches Under Data Scarcity

Abstract

Engineers predicting the behaviour of a physical system can now proceed in three ways: by deriving a model from first principles, by learning one from data, or by combining the two in a hybrid that embeds physical knowledge within a learned model. In practice, the selection among these approaches is often governed by disciplinary convention or by the availability of software rather than by the characteristics of the problem at hand. This paper develops a framework intended to make that selection a reasoned one. Drawing on recent literature in scientific machine learning, physics-informed neural networks, uncertainty quantification and model validation, and on reviews of hybrid modelling across structural, fluid, thermal, process, energy and materials engineering, it argues that the available approaches differ along three dimensions that bear directly on engineering practice: the quantity of data each requires, the reliability of its predictions beyond the conditions represented in that data, and the degree to which its predictions can be explained and justified. The appropriate choice is shown to depend on three properties of the application: how well the governing physics is understood, how much and what kind of data is available, and how costly a prediction error would be under extrapolation. The paper gives particular attention to validation, which cannot take the same form for a mechanistic model as for a learned one, and to engineering practice under data scarcity, a condition common across much of Africa, where it argues that physical knowledge constitutes the principal safeguard against models that appear accurate but are not.